| 1.46 | coherent derived unit | ||
| Derived unit that, for a given system of quantities and for a chosen set of base units, is a product of powers of base units with no other proportionality factor than one. | |||
| Note 1: | A power of a base unit is the base unit raised to an exponent. | ||
| Note 2: | Coherence can be determined only with respect to a particular system of quantities and a given set of base units. | ||
| Examples: | If the metre, the second, and the mole are base units, the metre per second is the coherent derived unit of velocity when velocity, v, is defined by the quantity equation v = dr/dt where r denotes distance and t time, and the mole per cubic metre is the coherent derived unit of amount-of-substance concentration when amount-of-substance concentration, c, is defined by the quantity equation c = n/V where n denotes amount of substance and V volume. The kilometre per hour and the knot are examples of derived units which are not coherent derived units in the International System of Quantities. | ||
| Note 3: | A derived unit can be coherent with respect to one system of quantities, but not to another. | ||
| Example: | The centimetre per second is the coherent derived unit of speed in the CGS system of units but is not a coherent derived unit in the SI. | ||
| Note 4: | The coherent derived unit for every derived quantity of dimension one in a given system of units is the number one, symbol 1. The name and symbol of the measurement unit one are generally not indicated. | ||
| Source: [VIM 1.12]. | |||
| 1.46 | coherent derived unit | ||
| Derived unit that, for a given system of quantities and for a chosen set of base units, is a product of powers of base units with no other proportionality factor than one. | |||
| Note 1: | A power of a base unit is the base unit raised to an exponent. | ||
| Note 2: | Coherence can be determined only with respect to a particular system of quantities and a given set of base units. | ||
| Examples: | If the metre, the second, and the mole are base units, the metre per second is the coherent derived unit of velocity when velocity, v, is defined by the quantity equation v = dr/dt where r denotes distance and t time, and the mole per cubic metre is the coherent derived unit of amount-of-substance concentration when amount-of-substance concentration, c, is defined by the quantity equation c = n/V where n denotes amount of substance and V volume. The kilometre per hour and the knot are examples of derived units which are not coherent derived units in the International System of Quantities. | ||
| Note 3: | A derived unit can be coherent with respect to one system of quantities, but not to another. | ||
| Example: | The centimetre per second is the coherent derived unit of speed in the CGS system of units but is not a coherent derived unit in the SI. | ||
| Note 4: | The coherent derived unit for every derived quantity of dimension one in a given system of units is the number one, symbol 1. The name and symbol of the measurement unit one are generally not indicated. | ||
| Source: [VIM 1.12]. | |||